PREFACE TO THE ENLARGED AND CORRECTED PRINTING vii

A striking characteristic of the elementary parts of analysis is the small
amount of algebra required. Effectively all that is needed is some elementary
linear algebra (which is included in an appendix at the end of the first volume,
for the reader's convenience). However, the role played by algebra increases in
the subsequent volumes, and we shall finally leave the reader at the point where
this role becomes preponderant, notably with the appearance of advanced
commutative algebra and homological algebra. As reference books in algebra
we have taken R. Godement's "Abstract Algebra," § and S. A. Lang's
"Algebra "If which we shall possibly augment in certain directions by means
of appendices.

As with the first volume, I have benefited greatly during the preparation of
this work from access to numerous unpublished manuscripts of N. Bourbaki
and his collaborators. To them alone is due any originality in the presentation
of certain topics.

Nice, France

April, 1969 J. DIEUDONN£

§ Godement, R., "Abstract Algebra." Houghton-Mifflin, New York, 1968. (Original
French edition published by Hermann, Paris, 1963.)

1[ Lang, S. A., "Algebra." Addison-Wesley, Reading, Massachusetts, 1965.ffective and usually easy to apply, for